Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cakz)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=27/8, b>=a

For fixed z and a=27/8, b=45/8

http://functions.wolfram.com/07.23.03.cakz.01

Input Form

Hypergeometric2F1[27/8, 45/8, -(9/2), z] == -((1/(1098752 (1 - z)^(27/2))) (Sqrt[1 - z] (-1098752 + 19228160 z - 170388108 z^2 + 1075168533 z^3 - 6210229998 z^4 + 59776498443 z^5 + 254707000100 z^6 + 164875170907 z^7 + 18187022898 z^8 - 273885403 z^9 + 7372420 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (-824064 + 14541296 z - 129819051 z^2 + 823751757 z^3 - 4764518083 z^4 + 122155304841 z^5 + 336076453851 z^6 + 183761410199 z^7 + 18323044047 z^8 - 277571613 z^9 + 7372420 z^10) Sin[(3 ArcSin[Sqrt[z]])/4]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]